Seeley suggests dancing is regulated by efficiency: \(\frac{gain-cost}{cost}\).
- Gain is determined by the nectar quality of the flower, \(q\).
- Cost is determined by the distance to the flower, \(x\).
- Energy gained is therefore \(\propto\) \(q\), cost increases linearly with \(x\).
- Can therefore refactor efficiency as: \(\frac{q}{1+\alpha x} - 1\), where \(\alpha\) is the energy spend per unit of distance.
- Energy spend cannot be negative, so the function must be positive:
\[\sigma(q,x) = [\frac{q}{1+\alpha x}-1]_+\]